We present results on the finite-time behavior of the discrete-time, finite-space version of the simulated annealing algorithm. The asymptotic and finite-time behavior of the annealing algorithm under slow cooling will be shown to depend on the largest eigenvalue of a certain matrix. To illustrate the utility of our results, we study the slowly cooled annealing algorithm applied to the maximum matching problem and demonstrate a polynomial randomized approximation property of the algorithm.

The line reversibility property of a two-stage multiserver system with manufacturing blocking has previously been established using a duality argument between the blocked state and the idle state. In this paper, we provide counterexamples that show this argument does not apply to systems with more than two stages. A focus of this paper is to provide a new proof for the result. Our argument is based on the duality between the service initiation and the service completion events.

This note studies the comparison of finite-buffer and nonexponential batch arrival systems of the form Gx/M/c/c + N with the corresponding systems, with N replaced by N', where N' can be smaller, larger, or infinite. If N' = ∞ the service times can be arbitrarily distributed. Both comparison and error bounds are obtained for performance measures such as the throughput, the idle probability, and the active server distribution. The results are of practical interest to establish computational reductions, either by infinite-space approximation or by reduced finite truncations. Two different proof techniques will be employed: the sample path approach and the Markov reward approach. The comparison of these two techniques is of interest in itself, showing the advantage and disadvantage of each.

We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.

We consider scheduling a single server in a multiclass queue subject to setup times and setup costs. We examine the issue of whether or not reductions in the mean and variance of the setup time distributions can lead to degraded system performance. Provided that setups are reduced according to a stochastically smaller ordering, we show that if an optimal policy is used both for the original system and for the system with reduced setup times, then an improvement in performance is guaranteed. Even in cases for which a truly optimal policy is unknown, idling can be employed to avoid degradation of performance as setup times are cut. We extend this approach to show that system performance is monotonic with respect to service time distributions, switching costs, holding costs, and uniform reductions in the arrival rates. Extensions to sequencedependent setups and job feedback are noted.

Stochastic automata networks (SANs) have recently received much attention in the literature as a means to analyze complex Markov chains in an efficient way. The main advantage of SANs over most other paradigms is that they allow a very compact description of the generator matrix by means of much smaller matrices for single automata. This representation can be exploited in different iterative techniques to compute the stationary solution. However, the set of applicable solution methods for SANs is restricted, because a solution method has to respect the specific representation of the generator matrix to exploit the compact representation. In particular, aggregation/disaggregation (a/d) methods cannot be applied in their usual realization for SANs without losing the possibility to exploit the compact representation of the generator matrix.

In this paper, a new a/d algorithm for SANs is introduced. The algorithm differs significantly from standard a/d methods because the parts to be aggregated are defined in a completely different way, exploiting the structure of the generator matrix of a SAN. Aggregation is performed with respect to single automata or sets of automata, which are the basic parts generating a SAN. It is shown that the new algorithm is efficient even if the automata are not loosely coupled.

The controlled Mx/G/1-type queueing model with two modes of operation is considered. The modes are characterized by different service time distributions and input rates. The switchover times are imposed in the model. The embedded stationary queue-length distribution and the explicit dependence of operation criteria on switchover levels are derived.

An efficient simulation estimator of the expected time until all states of a finite state semi-Markov process have been visited is determined.